Some switches support NTP as a server and client (equivalent to the PTP boundary clock), but there don't seem to be any using hardware timestamping. It's just the classic ntpd using software timestamps, good to few tens of microseconds at best.
And yes, NTP could definitely perform as well as PTP if the switches had a proper support. In my tests with directly connected NICs the synchronization is stable to few nanoseconds, same as with PTP. At the protocol level, they use the same timestamps.